On the Structure of Hopf Algebras
On the Structure of Hopf Algebras. By JOHN W. MILNOR and JOHN C. MOORE*. The notion of Hopf algebra' has been abstracted from the work of Hopf.
A primer of Hopf algebras
Here Hopf algebras play a dual role: first the (left) invariant differ- ential operators on an algebraic group form a cocommutative Hopf algebra which
Multiplier Hopf Algebras
MULTIPLIER HOPF ALGEBRAS. A. VAN DAELE. ABSTRACT. In this paper we generalize the notion of Hopf algebra. We consider an algebra A with or without identity
An Associative Orthogonal Bilinear Form for Hopf Algebras
FOR HOPF ALGEBRAS. By RICHARD GUSTAVUS LARSON * and Moss EISENBERG SWEEDLER. It is well-known that certain Hopf algebras contain non zero elements.
Introduction to Hopf algebras and representations
3 Algebras coalgebras
Semisimple Cosemisimple Hopf Algebras
Kaplansky has conjec- tured [1]: A finite-dimensional cosemisimple Hopf algebra is involutory. In this paper we show that if the characteristic of the ground
Hopf Algebras of Low Dimension
dimensional Hopf algebras. The key step of our approach will be the following. THEOREM 2.8. Let A be a Hopf algebra of dimension _< 11 that is not.
Integrals for Hopf Algebras
Integrals for Hopf algebras*. By Moss EISENBERG SWEEDLER. Introduction. For a Hopf algebra which is the "coordinate" ring of a compact Lie group.
A Very Basic Introduction to Hopf Algebras
There are many examples of familiar combinatorial objects which can be given the structure of a. Hopf algebra we look at a few simple examples at the end of
HOPF ALGEBRAS 1. Algebras and coalgebras 1.1. Algebras. We
A morphism of bialgebras f : A ? B is a linear map which is both an algebra and a coalgebra homomorphism. Page 4. 4. HOPF ALGEBRAS. 2.2. Test Lemmas. Lemma
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